Ayse Humeyra Bilge

(3+3+2) warped-like product manifolds with Spin(7) holonomy

Abstract We consider a generalization of eight-dimensional multiply warped product manifolds as a special warped product, by allowing the fiber metric to be non-block diagonal. We define this special warped product as a (3+3+2) warped-like manifold of the form M = F × B , where the base B is a two-dimensional Riemannian manifold, and the fibre F is of the form F = F 1 × F 2 where the F i ( i = 1 , 2 ) are Riemannian 3 -manifolds. We prove that the connection on M is completely determined by the requirement that the Bonan 4-form given in the work of Yasui and Ootsuka [Y. Yasui and T. Ootsuka, Spin ( 7 ) holonomy manifold and superconnection, Class. Quantum Gravity 18 (2001) 807–816] be closed. Assuming that the F i are complete, connected and simply connected, it follows that they are isometric to S 3 with constant curvature k > 0 and the Yasui–Ootsuka solution is unique in the class of (3+3+2) warped-like product metrics admitting a specific Spin ( 7 ) structure.

An Overview of the 2009 A(H1N1) Pandemic in Europe: Efficiency of the Vaccination and Healthcare Strategies

2009 A(H1N1) data for 13 European countries obtained from the weekly influenza surveillance overview (WISO) reports of European Centre for Disease Prevention and Control (ECDC) in the form of weekly cumulative fatalities are analyzed. The variability of relative fatalities is explained by the health index of analyzed countries. Vaccination and healthcare practices as reported in the literature are used to explain the departures from this model. The timing of the vaccination with respect to the peak of the epidemic and its role in the efficiency of the vaccination is discussed. Simulations are used to show that on-time vaccination reduces considerably the final value of R(t), R f, but it has little effect on the shape of normalized curve R(t)/R f.

On the uniqueness of epidemic models fitting a normalized curve of removed individuals

The susceptible-infected-removed (SIR) and the susceptible-exposed-infected-removed (SEIR) epidemic models with constant parameters are adequate for describing the time evolution of seasonal diseases for which available data usually consist of fatality reports. The problems associated with the determination of system parameters starts with the inference of the number of removed individuals from fatality data, because the infection to death period may depend on health care factors. Then, one encounters numerical sensitivity problems for the determination of the system parameters from a correct but noisy representative of the number of removed individuals. Finally as the available data is necessarily a normalized one, the models fitting this data may not be unique. We prove that the parameters of the (SEIR) model cannot be determined from the knowledge of a normalized curve of “Removed” individuals and we show that the proportion of removed individuals,

?Level grading? a new graded algebra structure on differential polynomials: application to the classification of scalar evolution equations

R(t)

Determination of epidemic parameters from early phase fatality data: A case study of the 2009 A (H1N1) pandemic in Europe

R(t), is invariant under the interchange of the incubation and infection periods and corresponding scalings of the contact rate. On the other hand we prove that the SIR model fitting a normalized curve of removed individuals is unique and we give an implicit relation for the system parameters in terms of the values of

A MATHEMATICAL DESCRIPTION OF THE CRITICAL POINT IN PHASE TRANSITIONS

R_m/R_f